Find the 5^("th ") term of the arithmetic sequence x+3,5x+5,9x+7,dots Answer:

Determine Common Difference: To find the 5th term of an arithmetic sequence, we need to determine the common difference between consecutive terms. Let's find the difference between the second and the first term. Difference = (5x + 5) - (x + 3)Calculate Difference: Now, let's calculate the difference. Difference = 5x + 5 - x - 3 Difference = 4x + 2 This is the common difference of the arithmetic sequence.Find 5th Term Formula: To find the 5th term, we need to add the common difference to the previous term three more times (since we already have the first two terms). The nth term of an arithmetic sequence can be found using the formula: nth term = first term + (n - 1) * common difference Let's apply this formula to find the 5th term.Substitute Values: Substitute the known values into the formula. 5th term = (x + 3) + (5 - 1) * (4x + 2) 5th term = (x + 3) + 4 * (4x + 2)Perform Multiplication and Addition: Now, let's perform the multiplication and addition to find the 5th term. 5th term = x + 3 + 16x + 8 5th term = 17x + 11 This is the 5th term of the arithmetic sequence.

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Find the
5^("th ") term of the arithmetic sequence
x+3,5x+5,9x+7,dots
Answer:

Find the $5^{\text {th }}$ term of the arithmetic sequence $x+3,5 x+5,9 x+7, \ldots$ $\newline$ Answer:

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Q. Find the

5^{\text {th }}

term of the arithmetic sequence

x+3,5 x+5,9 x+7, \ldots

\newline

Answer:

Determine Common Difference: To find the $5^{\text{th}}$ term of an arithmetic sequence, we need to determine the common difference between consecutive terms. $\newline$ Let's find the difference between the second and the first term. $\newline$ Difference = $(5x + 5) - (x + 3)$
Calculate Difference: Now, let's calculate the difference. $\newline$ Difference = $5x + 5 - x - 3$ $\newline$ Difference = $4x + 2$ $\newline$ This is the common difference of the arithmetic sequence.
Find $5$ th Term Formula: To find the $5^{th}$ term, we need to add the common difference to the previous term three more times (since we already have the first two terms). $\newline$ The $n^{th}$ term of an arithmetic sequence can be found using the formula: $\newline$ $n^{th}$ term = first term + $(n - 1) \times$ common difference $\newline$ Let's apply this formula to find the $5^{th}$ term.
Substitute Values: Substitute the known values into the formula. $\newline$ $5^{\text{th}}$ term $= (x + 3) + (5 - 1) \times (4x + 2)$ $\newline$ $5^{\text{th}}$ term $= (x + 3) + 4 \times (4x + 2)$
Perform Multiplication and Addition: Now, let's perform the multiplication and addition to find the $5^{\text{th}}$ term. $5^{\text{th}} \text{ term} = x + 3 + 16x + 8$ $5^{\text{th}} \text{ term} = 17x + 11$ This is the $5^{\text{th}}$ term of the arithmetic sequence.